Murthy 



The first integral is the known force due to the displacement below 

 the load waterline i. e. m 2 g . The second integral will however, 

 have to be evaluated. This is discussed below. 



As regards the strip SV , the integral becomes by expand- 

 ing the integrand about z' = and carrying out the integration as 

 before 



-2pge 10 J (s 2 6f 100 . r 01 +5 ^010 f OOl) 



* h dx. 



L 



We will now evaluate the correction for the hydrodynamic 

 pressure terms when substituted in (III. l). We will replace the 

 integration over S.j by that on the known surface S* together 

 with a correction denoting the integral over Si . The evaluation of 

 the integral over S.J' will be unnecessary as this raises the order 

 by Be or 0e 



The integrals are all of the form 



or 



//■ 



S 1o 



f(x' > z l ) ^ h , dx'dz' 



o x 



■ (x',z') -|^f dx'dz' 



Now, 



z'ro 



// f(x I z')-4-i i dx'dz' = / dx' / f(x'.z') 



5' 

 'o 



^h 



dz 1 



and when z = 



- - 2 



z' = x'd - z + 0(x d , e ) 



so that in view of the smallness of the range of integration, we may 

 replace the integrand by its value when z' = giving 



j(z -x'0) It (x' f z')-H, ] 



dx' 

 z=o 



194 



